There are 2 pairs of simultaneous equations of two variables. The technic is normally by eliminating one variable or by substution of one variable by another variable. Thus we reduce the variables to one single variable and one single equation and solve the unknown. And then use the given given equation by substituting the one value of the variable so found and find the value of the other variable.

1)

y=x+1..............................(i) and

y=-2x-4 ..........................(ii).

This is a pair of simultaneous equations with two variables, x and y. The left side of both equations are equal to y. Therefore, the right side must be equal:

x+1=-2x-4 or

x+2x=-1-4 =- 5 or

3x=-5 or x=-5/3. So from (1) y= x+1 = -5/3+1 =-2/3.

The method is as good as the substitution of y from 1st in to the 2nd.

It is not necessary that we should eliminate y 1st and we should solve for x first. But it is obviously easier to so.

y=x+1 or x=y-1 could be substited in the 2nd equation,y =-2x-4. So y=-2(y-1)-4 or y=-2y+2-4 or 3y =-2 or y= -2/3. And substituting in y=x+1 or in x=y-1, we get x=-2/3-1 =-5/3